My work consisted in understanding various proofs of an equality relating nonequilibrium measurements of work done on a system while changing an external parameter, to free energy differences, which are related to equilibrium states Jarzynski equality). To verify this result I simulated various trajectories of a Brownian particle in a quadratic potential, whose dynamics was governed by a Langevin equation (modelling a particle in contact with a heat reservoir at a given temperature), while performing a change in the stiffness of the potential between two values, in finite time. This change was done both in a linear manner, and by a protocol called ESE (Engineered Swift Equilibration) that allowed the system to be in equilibrium with the reservoir at the end of the switching of the stiffness.